1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Tom [10]
2 years ago
14

A certain industrial process yields a large number of steel cylinder whose lengths are distributed normally with mean 3.25 inche

s and standard deviation 0.05 inches. If two such cylinders are chosen at random and placed end to end what is the probability that their combined length is less than 6.60 inches? (round answer to two decimals)
Mathematics
1 answer:
Taya2010 [7]2 years ago
3 0

Answer:

Y = X_1 + X_2

If we find the expected value of Y we got:

E(Y) = E(X_1) + E(X_2) = 3.25 + 3.25 =6.5

And for the variance we assume that we have independent random variables for X1 and X2 so then we have:

Var(Y) = Var(X_1) + Var(X_2) = \sigma^2 + \sigma^2 = 2 \sigma^2 = 2*(0.05^2) = 0.005

And the deviation Sd(Y) = \sqrt{0.005}=0.0707

So then our random variable Y have the following distribution:

Y \sim N (\mu =6,5 , \sigma = 0.0707)

And we want to find this probability:

P(Y

And we can use the z score formula given by:

z=\frac{y -\mu_y}{\sigma_y}

And if we use the z score formula we got:

P(Y

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the lenghts of a population, and for this case we know the distribution for X is given by:

X \sim N(3.25,0.05)  

Where \mu=3.25 and \sigma=0.05

We slect two observations X_1, X_2

And let denote the combined lenght as:

Y = X_1 + X_2

If we find the expected value of Y we got:

E(Y) = E(X_1) + E(X_2) = 3.25 + 3.25 =6.5

And for the variance we assume that we have independent random variables for X1 and X2 so then we have:

Var(Y) = Var(X_1) + Var(X_2) = \sigma^2 + \sigma^2 = 2 \sigma^2 = 2*(0.05^2) = 0.005

And the deviation Sd(Y) = \sqrt{0.005}=0.0707

So then our random variable Y have the following distribution:

Y \sim N (\mu =6,5 , \sigma = 0.0707)

And we want to find this probability:

P(Y

And we can use the z score formula given by:

z=\frac{y -\mu_y}{\sigma_y}

And if we use the z score formula we got:

P(Y

You might be interested in
Please help because no one been answering my questions
never [62]

Answer:

BC = 8 \sqrt{2}

Step-by-step explanation:

\sin(45)  =  \frac{opposite}{hypotenuse}

\sin(45)  =  \frac{8}{BC}

(BC) \sin(45)  =  \frac{8}{x} (BC)

(BC) \sin(45)  = 8

\frac{(BC) \sin(45) }{ \sin(45) }  =  \frac{8}{ \sin(45) }

BC =  \frac{8}{ \sin(45) }

BC = 8 \sqrt{2}

5 0
3 years ago
Which graph models the function f(x) = -4(2)x?
scoray [572]
It is C. 

If you type in your calculator "Y=" and then " -4(2)^x " and click "GRAPH" you will see a descending graph, from left to right, that looks EXACTLY like the third graph in option C. 
5 0
3 years ago
Read 2 more answers
2<img src="https://tex.z-dn.net/?f=%5Csqrt%7Bx%2B5%7D%2B4%5C%5C" id="TexFormula1" title="\sqrt{x+5}+4\\" alt="\sqrt{x+5}+4\\" al
Andreyy89

2 \sqrt{x + 9}

8 0
2 years ago
Read 2 more answers
Brayden signed up for a streaming music service that costs $11 per month. The service allows Brayden to listen to unlimited musi
Vsevolod [243]

s = # of songs

y = total amount of money

$11 + $1(35) = y

Simplify the right side

$11 + $35 = y

Combine like terms

$46 = y

If he downloaded 35 songs, he would have ti pay $46

If he downloaded s amount of songs, he would have to pay $11 + $1s = y

4 0
3 years ago
Lesson 22 exit ticket
natita [175]
What about it. anything spesific?
5 0
3 years ago
Other questions:
  • Jacki plans to pay for the down payment of a new car with her credit card. The annual interest rate for her credit card is 17%.
    5·2 answers
  • What is twenty-six thousandths in decimal form
    9·2 answers
  • Determine the points for the graph of the relation y = -5x -3 using the x-values given in the table
    5·1 answer
  • The problem is attached &lt;3
    13·1 answer
  • Please help! Will mark brainliest
    12·1 answer
  • James is trying to determine the height of a building, so he uses a street sign as a reference. The street sign is 6 feet tall a
    12·2 answers
  • Help me answer the question ​
    12·2 answers
  • Does anyone know this answer??
    7·1 answer
  • Y=3x-4 and y= -x+2 to find the system of equations
    13·1 answer
  • PLEASE HELP!! The area of a square is 16 square units. Since 4^2 = 16 and (-4)^2 = 16, both 4 and -4 are square roots for 16. Ex
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!